26,940 research outputs found
Magnetic Z(N) symmetry in 2+1 dimensions
This review describes the role of magnetic symmetry in 2+1 dimensional gauge
theories. In confining theories without matter fields in fundamental
representation the magnetic symmetry is spontaneously broken. Under some mild
assumptions, the low-energy dynamics is determined universally by this
spontaneous breaking phenomenon. The degrees of freedom in the effective theory
are magnetic vortices. Their role in confining dynamics is similar to that
played by pions and sigma in the chiral symmetry breaking dynamics.
I give an explicit derivation of the effective theory in (2+1)-dimensional
weakly coupled confining models and argue that it remains qualitatively the
same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this
effective theory is a very simple classical statement about the long range
interaction between topological solitons, which follows (as a result of a
simple direct classical calculation) from the structure of the effective
Lagrangian. I show that if fundamentally charged dynamical fields are present
the magnetic symmetry becomes local rather than global. The modifications to
the effective low energy description in the case of heavy dynamical fundamental
matter are discussed. This effective lagrangian naturally yields a bag like
description of baryonic excitations. I also discuss the fate of the magnetic
symmetry in gauge theories with the Chern-Simons term
High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
We study theoretically the energy and spatially resolved local density of
states (LDoS) in graphene at high perpendicular magnetic field. For this
purpose, we extend from the Schr\"odinger to the Dirac case a
semicoherent-state Green's-function formalism, devised to obtain in a
quantitative way the lifting of the Landau-level degeneracy in the presence of
smooth confinement and smooth disordered potentials. Our general technique,
which rigorously describes quantum-mechanical motion in a magnetic field beyond
the semi-classical guiding center picture of vanishing magnetic length (both
for the ordinary two-dimensional electron gas and graphene), is connected to
the deformation (Weyl) quantization theory in phase space developed in
mathematical physics. For generic quadratic potentials of either scalar (i.e.,
electrostatic) or mass (i.e., associated with coupling to the substrate) types,
we exactly solve the regime of large magnetic field (yet at finite magnetic
length - formally, this amounts to considering an infinite Fermi velocity)
where Landau-level mixing becomes negligible. Hence, we obtain a closed-form
expression for the graphene Green's function in this regime, providing
analytically the discrete energy spectra for both cases of scalar and mass
parabolic confinement. Furthermore, the coherent-state representation is shown
to display a hierarchy of local energy scales ordered by powers of the magnetic
length and successive spatial derivatives of the local potential, which allows
one to devise controlled approximation schemes at finite temperature for
arbitrary and possibly disordered potential landscapes. As an application, we
derive general analytical non-perturbative expressions for the LDoS, which may
serve as a good starting point for interpreting experimental studies.Comment: 27 pages, 2 figures ; v2: typos corrected, corresponds to published
versio
Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling
We theoretically investigate the spectral properties and the spatial
dependence of the local density of states (LDoS) in disordered two-dimensional
electron gases (2DEG) in the quantum Hall regime, taking into account the
combined presence of electrostatic disorder, random Rashba spin-orbit in-
teraction, and finite Zeeman coupling. To this purpose, we extend a
coherent-state Green's function formalism previously proposed for spinless 2DEG
in the presence of smooth arbitrary disorder, that here incorporates the
nontrivial coupling between the orbital and spin degrees of freedom into the
electronic drift states. The formalism allows us to obtain analytical and
controlled nonperturbative expressions of the energy spectrum in arbitrary
locally flat disorder potentials with both random electric fields and Rashba
coupling. As an illustration of this theory, we derive analytical microscopic
expressions for the LDoS in different temperature regimes which can be used as
a starting point to interpret scanning tunneling spectroscopy data at high
magnetic fields. In this context, we study the spatial dependence and linewidth
of the LDoS peaks and explain an experimentally-noticed correlation between the
spatial dispersion of the spin-orbit splitting and the local extrema of the
potential landscape.Comment: 18 pages, 5 figures; typos corrected and Sec. IV A rewritten;
published versio
Vortices in a Bose-Einstein condensate confined by an optical lattice
We investigate the dynamics of vortices in repulsive Bose-Einstein
condensates in the presence of an optical lattice (OL) and a parabolic magnetic
trap. The dynamics is sensitive to the phase of the OL potential relative to
the magnetic trap, and depends less on the OL strength. For the cosinusoidal OL
potential, a local minimum is generated at the trap's center, creating a stable
equilibrium for the vortex, while in the case of the sinusoidal potential, the
vortex is expelled from the center, demonstrating spiral motion. Cases where
the vortex is created far from the trap's center are also studied, revealing
slow outward-spiraling drift. Numerical results are explained in an analytical
form by means of a variational approximation. Finally, motivated by a discrete
model (which is tantamount to the case of the strong OL lattice), we present a
novel type of vortex consisting of two pairs of anti-phase solitons.Comment: 10 pages, 6 figure
Thermal vortex dynamics in thin circular ferromagnetic nanodisks
The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft
ferromagnetic material is considered. The demagnetization field is calculated
using two-dimensional Green's functions for the thin film problem and fast
Fourier transforms. At zero temperature, the dynamics of the
Landau-Lifshitz-Gilbert equation is simulated using fourth order Runge-Kutta
integration. Pure vortex initial conditions at a desired position are obtained
with a Lagrange multipliers constraint. These methods give accurate estimates
of the vortex restoring force constant and gyrotropic frequency, showing
that the vortex core motion is described by the Thiele equation to very high
precision. At finite temperature, the second order Heun algorithm is applied to
the Langevin dynamical equation with thermal noise and damping. A spontaneous
gyrotropic motion takes place without the application of an external magnetic
field, driven only by thermal fluctuations. The statistics of the vortex radial
position and rotational velocity are described with Boltzmann distributions
determined by and by a vortex gyrotropic mass ,
respectively, where is the vortex gyrovector.Comment: 18 pages, 17 figure
Dynamics of Non-Abelian Vortices
The scattering is studied using moduli space metric for well-separated
vortices of non-Abelian vortices in (2+1)-dimensional U(N) gauge theories with
N Higgs fields in the fundamental representation. Unlike vortices in the
Abelian-Higgs model, dynamics of non-Abelian vortices has a lot of new
features; The kinetic energy in real space can be transfered to that of
internal orientational moduli and vice versa, the energy and charge transfer
between two vortices, the scattering angle of collisions with a fixed impact
parameter depends on the internal orientations, and some resonances appear due
to synchronization of the orientations. Scattering of dyonic non-Abelian
vortices in a mass deformed theory is also studied. We find a bound state of
two vortices moving along coils around a circle, like a loop of a phone code.Comment: 45 pages, 13 figure
Surface Roughness Dominated Pinning Mechanism of Magnetic Vortices in Soft Ferromagnetic Films
Although pinning of domain walls in ferromagnets is ubiquitous, the absence
of an appropriate characterization tool has limited the ability to correlate
the physical and magnetic microstructures of ferromagnetic films with specific
pinning mechanisms. Here, we show that the pinning of a magnetic vortex, the
simplest possible domain structure in soft ferromagnets, is strongly correlated
with surface roughness, and we make a quantitative comparison of the pinning
energy and spatial range in films of various thickness. The results demonstrate
that thickness fluctuations on the lateral length scale of the vortex core
diameter, i.e. an effective roughness at a specific length scale, provides the
dominant pinning mechanism. We argue that this mechanism will be important in
virtually any soft ferromagnetic film.Comment: 4 figure
- …